function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


h = sigmoid(X * theta);
cost = (-y .* log(h)) - ((1-y) .* (log(1-h)));

%J = 1/m * (sum(cost)) + (lambda * theta.^2);
J = 1/m * (sum(cost));
J = J + (lambda/(2*m) * sum(theta(2:end).^2));

grad = 1/m * ((h-y)' * X)';
grad_0 = grad(1);
grad_rest = grad(2:end);
grad_rest = grad_rest + (lambda/m)*theta(2:end);
grad(2:end) = grad_rest;

% =============================================================

end
